From science to arts, IDNLearn.com has the answers to all your questions. Join our interactive community and access reliable, detailed answers from experienced professionals across a variety of topics.

Suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is between 57 and 65? Round youranswer to the nearest tenth of a percent.

Suppose A Normal Distribution Has A Mean Of 62 And A Standard Deviation Of4 What Is The Probability That A Data Value Is Between 57 And 65 Round Youranswer To T class=

Sagot :

SOLUTION

From the given data the mean is 62 and standard deviation is 4

It is required to find the probability that a data value is between 57 and 62

That is:

[tex]P(57\lt x\lt65)[/tex]

The z scores is calculated using:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the x values it follows:

[tex]z=\frac{57-62}{4}=-1.25[/tex]

Also,

[tex]z=\frac{65-62}{4}=0.75[/tex]

Thus the required probability is:

[tex]P(-1.25The proability is:[tex]P(-1.25This can be expressed as percentage as:[tex]P(-1.25\lt z\lt0.75)=66.8\%[/tex]

Therefore the correct option is C

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.